Umaima is 20 years younger than Omar. Omar and Umaima first met 3 years ago. Twenty years ago, Omar was 5 times older than Umaima. How old is Omar now?
Solution: We can use the given information to write down two equations that describe the ages of Omar and Umaima. Let Omar's current age be $o$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $o = u + 20$ Twenty years ago, Omar was $o - 20$ years old, and Umaima was $u - 20$ years old. The information in the second sentence can be expressed in the following equation: $o - 20 = 5(u - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $o$ , it might be easiest to solve our first equation for $u$ and substitute it into our second equation. Solving our first equation for $u$ , we get: $u = o - 20$ . Substituting this into our second equation, we get the equation: $o - 20 = 5($ $(o - 20)$ $ -$ $ 20)$ which combines the information about $o$ from both of our original equations. Simplifying the right side of this equation, we get: $o - 20 = 5o - 200$ Solving for $o$ , we get: $4 o = 180$ $o = 45$.